Chelation removes multiple minerals)metals, not just the one you're targeting. Chelation got a bad name early on as people became depleted in "good" minerals which are cofactors needed in many essential biochemical processes, and things stopped working. It can lead to death... If you are chelating, it would be wise to replenish minerals lost in the process. It at the very least, test your mineral status from time to time.
As for vitamin C, I chelated on and off for 8 years using multiple methods and I've used high dose vitamin C for cancer and infections, but never used vitamin C for chelation. It does help recycle glutathione, so that would be helpful, but ALA, DMSA, DMSO, DMPS, etc., depending on what sort of toxicity you have, are more effective.
And, working with a practitioner experienced in chelation and setting up supportive nutrient programs would be prudent, helping you to avoid serious problems caused by naive mistakes.